PROBLEM 5: z-interval with normal curve plot The shade.norm.c function (provided at the end of this document) requires you to input the SE of the sample average. Modify this function in R so that it computes the SE for you. That is, modify the function so that it takes the following four inputs (you choose the order and the names): average, SD, sample size, confidence level a) Paste the code. b) Use the function to solve this typical statistics problem: a certain county's residents have an unknown average income. A research team wishes to estimate this unknown average. They obtain a simple random sample of 500 residents of the county. For this sample, the average salary is $58,420. The SD of the sample is $22,840. Set up a 90% confidence interval for the unknown average salary. Provide the estimate, the margin of error, and the plot illustrating the interval. c) Is the confidence level exact or approximate? Why? d) Is the standard error known or estimated from the data? Why? e) What does the confidence refer to? (It is the chance that...)PROBLEM 5: z-interval with normal curve plot The shade.norm.c function (provided at the end of this document) requires you to input the SE of the sample average. Modify this function in R so that it computes the SE for you. That is, modify the function so that it takes the following four inputs (you choose the order and the names): average, SD, sample size, confidence level a) Paste the code. b) Use the function to solve this typical statistics problem: a certain county's residents have an unknown average income. A research team wishes to estimate this unknown average. They obtain a simple random sample of 500 residents of the county. For this sample, the average salary is $58,420. The SD of the sample is $22,840. Set up a 90% confidence interval for the unknown average salary. Provide the estimate, the margin of error, and the plot illustrating the interval. c) Is the confidence level exact or approximate? Why? d) Is the standard error known or estimated from the data? Why? e) What does the confidence refer to? (It is the chance that...)